Trump's comments in the interview are an extraordinary criticism of a foreign leader during a trip to that leader's country. Trump was greeted by May in a ceremony full of pomp and circumstance Thursday evening just hours before the interview was released.

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Trump's interview with the paper came after his contentious meeting with NATO members in Brussels and ahead of his scheduled visit with Queen Elizabeth II. His interview likewise came after May recently announced a path forward on Brexit that met criticism from members of her own government, including Boris Johnson, who resigned as foreign secretary on Monday.

Trump told The Sun he felt her approach of keeping some ties to the EU would "affect trade with the United States, unfortunately in a negative way," and referenced his administration's combative trade posture with the EU.

"If they do a deal like that, it will most likely, because we'll be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal," Trump said.

He added, "If they do that, their trade deal with the US will probably not be made because we have enough difficulty with the European Union."

As for Johnson, Trump called him "a very talented guy," lamented his resignation and, while couching his comment in regard to May, said Johnson would make a good head of government.

"I'm just saying I think he would be a great prime minister," Trump said. "I think he's got what it takes, and I think he's got the right attitude to be a great prime minister."

Immigration and London Mayor Sadiq Khan

Trump, whose hardline immigration policies have included the recent "zero tolerance" policy that led to the separation of immigrant families, bemoaned migration flows into Europe, calling the changing population there "a shame."

"I think the immigration, allowing the immigration to take place in Europe is a shame," Trump said. "I think it changed the fabric of Europe, and unless you act very quickly, it's never going to be what it was, and I don't mean that in a positive way. So I think allowing millions and millions of people to come into Europe is very, very sad. I think you're losing your culture."

The interview also touched on London Mayor Sadiq Khan, who Trump has criticized, including in the wake of apparent terrorist attacks on the UK's capital city.

"You have a mayor who has done a terrible job in London," Trump said, adding later that Khan had "done a very bad job on terrorism."

Trump reacted to the protests to his UK trip by telling The Sun there is "no reason for me to go to London."

"I used to love London as a city," Trump said. "I haven't been there in a long time."

White House press secretary Sarah Sanders said Trump's interview shows he really does like May.

"The President likes and respects Prime Minister May very much," Sanders said. "As he said in his interview with the Sun she 'is a very good person' and he 'never said anything bad about her.' He thought she was great on NATO today and is a really terrific person. He is thankful for the wonderful welcome from the Prime Minister here in the UK."